HELM (continued)

Amongst the several angles that the rudder makes with the keel, there is always one position more favourable than any of the others, as it more readily produces the desired effect of turning the ship, in order to change her course. To ascertain this, it must be considered, that if the obliquity of the rudder with the keel is greater than the obtuse angle A B D, so as to diminish that angle, the action of the water upon the rudder will increase, and at the same time oppose the course of the ship in a greater degree; because the angle of incidence will be more open, so as to present a greater surface to the shock of the water, by opposing it's passage more perpendicularly. But at that time the direction N P of the effort of the helm upon the ship will pass, with a smaller distance from the center of gravity G towards R, and less approach the perpendicular N L, according to which it is absolutely necessary that the power applied should act with a greater effect to turn the vessel. Thus it is evident that if the obtuse angle A B D is too much inclosed, the greatest impulse of the water will not counterbalance the loss sustained by the distance of the direction N P from N L; or by the great obliquity, which is given to the same direction N P of the absolute effort of the helm with the keel A B. If, on the contrary, the angle A B D is too much opened, the direction N P of the force of action of the helm will become more advantageous to turn the vessel, because it will approach nearer the perpendicular N L; so that the line prolonged from N P will increase the line G R, by removing R to a greater distance from the center of gravity G: but then the helm will receive the impression of the water too obliquely, for the angle of incidence will be more acute; so that it will only present a small portion of it's breadth to the shock of the water, and by consequence will only receive a feeble effort. By this principle it is easy to conceive, that the greatest distance G R from the center of gravity G is not sufficient to repair the diminution of force occasioned by the too great obliquity of the shock of the water. Hence we may conclude, that when the water either strikes the helm too directly, or too obliquely, it idles a great deal of the effect it ought to produce. Between the two extremities there is therefore a mean position, which is the most favourable to it's operations.

The diagonal N P of the rectangle I L represents the absolute direction of the effort of the water upon the helm. N I expresses the portion of this effort which is opposed to the ship's head-way, or which pushes her astern, in a direction parallel to the keel. It is easily perceived that this part N I of the whole power of the helm contributes but little to turn the vessel; for if I N is prolonged, it appears that it's direction approaches to a very small distance G V from the center of gravity G, and that the arm of the lever B N = G V, to which the force is applied, is not in the whole more than equal to half the breadth of the rudder: but the relative force N L, which acts perpendicular to the keel, is extremely different. If the first N I is almost useless, and even pernicious, by retarding the velocity; the second N L is capable of a very great effect, because it operates at a considerable distance from the center of gravity G of the ship, and acts upon the arm of a lever G E, which is very long. Thus it appears, that between the effects N L and N I, which result from the absolute effort N P there is one which always opposes the ship's course, and contributes little to her motion of turning; whilst the other produces only this movement of rotation, without operating to retard her velocity (Bourdé, Manoeuvrier).

Geometricians have determined the most advantageous angle made by the helm with the line prolonged from the keel, and fixed it at 54° 44 presuming that the ship is as narrow at her floating-line, or at the line described by the surface of the water round her bottom, as at the keel. But as this supposition is absolutely false, inasmuch as all vessels augment their breadth from the keel upward to the extreme breadth, where the floating-line or the highest water-line is terminated; it follows that this angle is too large by a certain number of degrees. For the rudder is impressed by the water, at the heighth of the floating-line, more directly than at the keel, because the fluid exactly follows the horizontal outlines of the bottom; so that a particular position of the helm might be supposed necessary for each different incidence which it encounters from the keel upwards. But as a middle position may be taken between all these points, it will be sufficient to consider the angle formed by the sides of the ship, and her axis, or the middle-line of her length, at the surface of the water, in order to determine afterwards the mean point, and the mean angle of incidence.